Question

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):

Answer 1

Consider a ship of known base area floating in the sea. Measure its depth in sea (say d₁).

Volume of water displaced by the ship, V_b = A d₁

Now, move an elephant on the ship and measure the depth of the ship (d₂) in this case.

Volume of water displaced by the ship with the elephant on board, V_be= Ad₂

Volume of water displaced by the elephant = Ad₂ – Ad₁

Density of water = D

Mass of elephant = AD (d₂ – d₁)

Answer 2

Measure the depth of an empty boat in water. Let it be d1. If A be the base area of the boat, then volume of water displaced by boat, V1 = Ad2

Let d2 be the depth of boat in water when the elephant is moved into the boat. Volume of water displaced by (boat + elephant), V2 = Ad2 Volume of water displaced by elephant,

V = V2-V1 = A(d2 -d1)

If p be the density of water, then mass of elephant = mass of water displaced by it = A(d2 – d1) p.